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Grade 6
Arithmetic
Meet 2
2009-2010
1)
How many whole numbers lie in the interval between ⅝ and 2π?
Answer: _________________ (2 pts)
2)
The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160.
There’s a service center on the highway located three fourths of the way from the third exit to
the tenth exit. At what milepost would you expect to find this service center?
Answer: _________________(3 pts)
3)
Will, Phil, Bill, Lil, and Jill have different amounts of money. Neither Lil nor Will has as much
money as Bill. Both Will and Phil have more money than Jill. Lil has more than Jill, but less
than Will. Who has the least amount of money?
Answer: _________________(4 pts)
4)
If 4 * 3 = 13 and 7 * 8 = 20, what is 15* 5?
Answer: _________________(5 pts)
5)
A complete cycle of a traffic light takes 45 seconds. During each cycle, the light is green for 17
seconds, yellow for 3 seconds, and red for 25 seconds. Of the next 180 cars through the
intersection, how many would expect to not get a green light?
Answer: _____________cars (6 pts)
Grade 6
Geometry
Meet 2
2009-2010
1)
In triangle CAT, we have m  ACT = m  ATC and m  CAT = 36°. If line segment TR bisects
 ATC, then find the measure of  CRT.
A
R
C
2)
Answer: ________________° (2 pts)
T
Figure ABCD is a square. Inside this square, three smaller squares are drawn with side lengths
as labeled. Find the area of the shaded L-shaped region. Note: Figure is NOT drawn to scale.
D
A
1
3
3
C
3)
1
Answer: ___________units2 (3 pts)
B
Find the supplement of the complement of a 17° angle.
Answer: _____________units (4 pts)
4)
The degree measure of angle A is:
A
100
110
40
Answer: ________________° (5 pts)
5)
Kevin has a pool in his backyard in the shape of a rectangular prism. He wants to know the
dimensions of his pool, but does not have an adequate measuring device. From past years, he
knows it holds 1728 cubic feet of water. Using a piece of string, he determined that the width is
twice the depth, and the length is twice the width of the pool. What is the length of the pool?
Answer: _____________ feet (6
pts)Grade
6
Team
Meet 2
2009-2010
1)
Barbara decided to clean out her sweater drawer. She has a box that is 1 ft x 1.5 ft x 3 ft. If she
folded all her sweaters into a 12 in x 18 in x 3 in size, how many could she fit into the box?
Answer: _________________ (6 pts)
2)
Leo was 100 meters from home and Leo’s dog Shadow was 80 meters from home. It took Leo
twice as long as Shadow to reach home. If Shadow runs 10 meters per minute, how fast did Leo
run in meters per minute? Write your answer as a mixed number in simplest form.
Answer: ________________meters per min (6 pts)
3)
A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden
larger, while using the same fence, its shape is changed to a square. By how many square feet
does this enlarge the garden?
Answer: _____________sq ft (6 pts)
4)
Of the 36 students in Brynn’s class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer
blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. If Brynn
showed this data on a pie graph, how many degrees would she use to show the cherry pie?
Answer: _________________(6 pts)
5)
In trapezoid ABCD, the sides AB and CD are congruent. The perimeter of ABCD is?
8
B
C
3
A
D
16
Answer: _________________(6 pts)
6)
Points A, B, C, and D have coordinates, A(3, 2), B(3, -2), C(-3, -2) and D(-3, 0). The area of
quadrilateral ABCD is?
Answer: _________________(6 pts)
Grade 6
Solutions
Meet 2
2009-2010
Arithmetic
1) 6
2) 130
The smallest whole number in the interval is 1 because 5/8 is less than 1. The largest
whole number in the interval is 6 because 2π is more than 6 but less than 7. There are six
whole numbers in the interval. They are: 1, 2, 3, 4, 5, and 6.
There are 160 – 40 = 120 miles between the third and tenth exits, so the service center is
at milepost 40 + (¾) 120 = 40 + 90 = 130
3) Jill
4) 55
5) 112 cars
From the 2nd sentence, Bill has more than someone, so he can’t have the least. From the
3rd sentence, both Will and Phil have more than someone, so that eliminates them. And
from the 4th sentence, Lil has more than someone, so that leaves only Jill.
The pattern is to multiply the first number by 4, then subtract the second number. 4 x 4 =
16, 16-3=13; 7 x 4 = 28, 28-8=20; 15 x 4 = 60, 60-5=55.
The probability of green is 17/45, so the probability of not green is 1 – 17/45 = 28/45.
180 x 28/45 = 112.
Geometry
1) 72°
2) 7
3) 107°
4) 30°
5) 24
Since <ACT = <ATC and <CAT = 36°, we have 2 ( <ATC) = 180° - 36° = 144° and
<ATC = <ACT = 72°. Because line segment TR bisects <ATC, CTR = ½ (72°) = 36°.
In triangle CRT, <CRT = 180° - 36° - 72° = 72°
The L-shaped region can be decomposed into a 4 x 1 rectangle and a 3 x 1 rectangle. So
the total area is 7.
90 – 17 = 73, 180 – 73 = 107.
The angles of the small outer triangle with 40° are both 70° (180 – 110 = 70, etc.). So the
angle between the 110° and 100° angles is also 110° making the angles of the triangle
with angle A equal to 70° and 80°. 180 – 150 = 30°.
If depth = Y, then width = 2Y and length is 2 x 2 x Y or 4Y. This means that: Y x 2Y x
4Y = volume. 8Y³ = volume, 8Y³ = 1728, Y³ = 216, Y = 6. Since length = 4Y, length =
4 x 6 = 24.
Team
1’ x 1.5’ x 2’ = 12” x 18” x 36”. The 12” and 18” are the same as the sweater. 12 x 3
=36”.
2) 6 ¼ m/min It takes Shadow 8 minutes to go 80 meters at 10 meters/minute. It takes Leo twice as
long, so 16 minutes. Leo went 100 meters in 16 minutes, so 100/16 = 6 ¼ meters/min.
3) 400 sq ft The area of the garden was 500 square feet (50 x 10), and its perimeter was 120 ft, (2 x
(50+10)). The square garden is also enclosed by 120 feet of fence, so its sides are each
30 feet long. The square gardens area is 900 sq. feet (30 x 30) and this has increased the
garden area by 400 sq. ft.
4) 50°
Since 12 + 8 + 6 = 26 there are 36-26 = 10 children who prefer cherry or lemon pie.
These ten are divided in equal parts of 5 each. 5/36 x 360° = 5 x 10° = 50°
5) 34
When the figure is divided as shown in the problem, the unknown sides are the
hypotenuses of right triangles with legs of 3 and 4. Using the Pythagorean Theorem
gives AB = CD = 5. The total perimeter is: 16 + 5 + 8 + 5 = 34
6) 18
The lower part is a 6 x 2 rectangle with area 12. The upper part is a triangle with base 6
and altitude 2 with area 6. Total area is: 12 + 6 = 18.
1) 12